Problem: Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{x^5+6x+2}{x}=\dfrac{x^5}{x}+\dfrac{6x}{x}+\dfrac{2}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{x^5}{x}&=x^4 \\\\ \dfrac{6x}{x}&=6 \end{aligned}$ $\dfrac{2}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $x^4+6+\dfrac{2}{x}$ [I want to see a different way of performing the division.]